Add the milk as soon as you make the coffee.

Why this works (intuition)

• Hot liquids lose heat faster when they’re much hotter than the room (Newton’s law of cooling).
• If you wait, the black coffee stays hotter for longer and sheds heat quickly.
• If you add milk now, the temperature drops a bit immediately, so the drink spends the wait at a lower temperature and loses heat more slowly.
• Bonus: adding milk early also reduces evaporation, which further cuts heat loss.

Back-of-the-envelope math

Let coffee (mass m_c, heat capacity c_c) start at T_c0, milk (mass m_m, heat capacity c_m) at T_m, room at T_a, and cooling rate constant k.

1. Add milk immediately: mix to T₀ = (m_c c_c T_c0 + m_m c_m T_m)/(m_c c_c + m_m c_m), then cool for time t: T_now(t) = T_a + (T₀ - T_a)e^{-kt}.
2. Add milk at the end: cool coffee alone to T_c(t) = T_a + (T_c0 - T_a)e^{-kt}, then mix: T_late(t) = [m_c c_c T_c(t) + m_m c_m T_m]/(m_c c_c + m_m c_m).

For the same t, algebra shows T_now(t) ≥ T_late(t) whenever the milk is no hotter than the room (true for fridge or room-temp milk). Equality only in trivial cases.

Practical tips

• Add milk early if you want the hottest drink later.
• Cover the cup to suppress evaporation (keeps it hotter either way).
• Don’t blow/stir during the wait if heat retention is the goal.
• If you can also warm the milk a bit first, it’ll be hotter still.

Edge cases

• If the milk were somehow hotter than the coffee (rare), adding it later could help; otherwise, early is best.
• If you’ll drink immediately, timing doesn’t matter—only the mixed temperature does.